Research
 

 My Master thesis:  "Decompositions and representations of monotone operators with linear
graphs"( Thesis latex file and  PDF file).

My PhD thesis:  "On Monotone Linear Relations and the Sum Problem in Banach Spaces"
(PDF file).

 

 1. Heinz H. Bauschke,  Xianfu Wang and Liangjin Yao,  "Autoconjugate representers for linear monotone operators",  Mathematical Programming (Series B) 123, pp. 5-24, 2010. (56published.pdf).

 2.  Heinz H. Bauschke,  Xianfu Wang and Liangjin Yao , " Monotone linear relations: maximality and Fitzpatrick functions",  Journal of Convex Analysis 16, 673–686, 2009 (jca0822_b.pdf).

  3.   Heinz H. Bauschke,  Xianfu Wang and Liangjin Yao,    " General resolvents for monotone operators: characterization and extension'' ,  Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems (Huangguoshu 2008), to appear (conference_ch04 1.pdf).

4. Heinz H. Bauschke,  Xianfu Wang and Liangjin Yao,  "An answer to S.\ Simons' question
on the maximal monotonicity of the sum of a maximal monotone linear operator and a normal cone operator
",   Set-Valued and Variational Analysis 17, pp. 195-201, 2009.(June19.pdf).

5.  Liangjin Yao,  "The Brezis-Browder Theorem revisited and properties of Fitzpatrick functions of order n",
Fixed Point Theory for Inverse Problems in Science and Engineering
(Banff 2009) , Springer-Verlag,  Springer-Verlag,  49, pp. 391--402, 2011
(Banff).

6. Heinz H. Bauschke,  Xianfu Wang and Liangjin Yao,  "Examples of discontinuous
maximal monotone linear operators and the solution to a recent problem posed by B.F. Svaiter
",

Journal of Mathematical Analysis and Applications 370, pp. 224-241, 2010 (JMAA.pdf).

7. Liangjin Yao,  "An affirmative answer to a problem posed by Zalinescu'',

  Journal of Convex Analysisvol18, 621--626, 2011   (June2001.pdf).

 8. Heinz H. Bauschke,  Xianfu Wang and Liangjin Yao,  "On Borwein-Wiersma Decompositions of monotone linear relations
", 
SIAM Journal on Optimization 20, pp. 2636-2652, 2010(Decom2772.pdf)

9. Heinz H. Bauschke,  Xianfu Wang and Liangjin Yao,  "On the maximal monotonicity of the sum  of a maximal monotone linear relation  and the subdifferential operator of a sublinear function",
to appear Proceedings of the Haifa Workshop on Optimization Theory and Related Topics.
Contemp. Math., Amer. Math. Soc., Providence, RI
. (1001.0257v1.pdf)

10.  Liangjin Yao,  "The sum of a maximal monotone operator  of type (FPV) and a maximal monotone operator
with full domain is maximal monotone
", Nonlinear Analysis
74, pp. 6144--6152, 2011 (1005.2247v2.pdf).


11.  Liangjin Yao,  ``The sum of a maximally monotone linear relation and the subdifferential of a proper lower semicontinuous  convex function is maximally monotone'', Set-Valued and Variational Analysis 20, pp.~155--167, 2012
 (Linear Relation)


12.  Xianfu Wang and Liangjin Yao, ``Maximally monotone linear subspace extensions of monotone subspaces:
Explicit constructions and characterizations'',  Mathematical Programming (Series B), in press
 (LinearExtension.pdf)


13. Heinz H Bauschke, Jonathan M. Borwein, Xianfu Wang, and Liangjin Yao,``For maximally monotone linear relations,
dense type, negative-infimum type, and Fitzpatrick-Phelps type all coincide with monotonicity of the adjoint'' ,
 (1103.6239v1.pdf) merged with (Brezis-Browder) in Journal of Functional Analysis.


14. Heinz H Bauschke, Jonathan M. Borwein, Xianfu Wang, and Liangjin Yao,``Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type D'',  Optimization Letters, vol. 6, pp. 1875--1881, 2012. (1104.0750v1.pdf)


15: Heinz H Bauschke, Jonathan M. Borwein, Xianfu Wang, and Liangjin Yao,``Construction of pathological maximally monotone operators on non-reflexive Banach spaces'',  Set-Valued and Variational Analysis 20, pp.~387--415, 2012.
(1108.1463v1.pdf)

16: Heinz H Bauschke, Jonathan M. Borwein, Xianfu Wang, and Liangjin Yao,``Monotone operators and ``bigger conjugate'' functions'',  Journal of Convex Analysis, vol. 20, pp.143--155, 2013.
(1108.2578v1.pdf)


17: Jonathan M. Borwein, Regina Burachik, and Liangjin Yao, ``Monotone operators without enlargements'',
Proceedings of the Workshop on Computational and Analytical Mathematics in Honour of Jonathan Borwein’s 60th Birthday}, Springer
  (Enlargement)

18: Heinz H Bauschke, Jonathan M. Borwein, Xianfu Wang, and Liangjin Yao,``The Brezis-Browder Theorem in a general Banach space'', Journal of Functional Analysis 262, pp.~4948--4971, 2012
 (Brezis-Browder)


19: Heinz H. Bauschke,  Xianfu Wang and Liangjin Yao,  "Rectangularity and paramonotonicity of maximally monotone operators", Optimization, vol. 63, pp. 487–504, 2014.
 (RectPara)

20: Jonathan M. Borwein and Liangjin Yao, ``Structure theory for maximally monotone operators with points of continuity'',  Journal of Optimization Theory and Applications , vol 156, pp. 1--24, 2013 (Invited paper)
 (max structure)


21: Jonathan M. Borwein and Liangjin Yao, ``Some results on the convexity of the closure of the
domain of a maximally monotone operator'', Optimization Letters, vol. 8, pp. 237–246, 2014.
 (nearly convex domain)


22:  Jonathan M. Borwein and Liangjin Yao, ``Legendre-type integrands and convex integral functions'',
Journal of Convex Analysis, in press ( Legendre function)


23:  Jonathan M. Borwein and Liangjin Yao, ``Recent progress on  Monotone Operator Theory'',
Infinite Products of Operators and Their Applications, Contemporary Mathematics,vol. 636,
pp. 51–81, 2015. (Survey Mono)


24: Jonathan M. Borwein, Regina Burachik, and Liangjin Yao, ``Conditions for zero duality gap in convex programming'',
Journal of Nonlinear and Convex Analysis, vol 15, pp. 167–190, 2014. (Duality map)

25: Jonathan M. Borwein and Liangjin Yao, ``Maximality of the sum of a maximally monotone linear relation and a
maximally monotone operator'', Set-Valued and Variational Analysis, vol. 21, pp. 603–616, 2013.  (LinearSum)


26: Francisco J. Aragon Artacho, Jonathan M. Borwein,Victoria Martin-Marquez, and Liangjin  Yao,
``Applications of Convex Analysis within Mathematics'',  Mathematical Programming (Se-
ries B), vol. 148, pp. 49–88, 2014. (ACAM)



27: Jonathan M. Borwein, Guoyin Li, and Liangjin Yao, Analysis of the convergence rate for the
cyclic projection algorithm applied to semi-algebraic convex sets", SIAM Journal on
Optimization, vol. 24, pp. 498–527, 2014. (cyclic projections)

28:   Jonathan M. Borwein and Liangjin  Yao,``Sum theorems  for maximally monotone operators of type (FPV)'',
Journal of the Australian Mathematical Society, vol. 97, pp 1–26, 2014. (FPVsum)


29.  Liangjin Yao,“ Finer properties of ultramaximally monotone operators on Banach spaces”,
Journal of Convex Analysis, vol. 23, 2016. (UltraMaxi)

30.  Liangjin Yao, “Maximality of the sum of the subdifferential operator and a maximally mono-
tone operator”, Linear and Nonlinear Analysis, vol. 1, pp. 95–108, 2015. (Subdsum)

31. Anthony To-Ming Lau and Liangjin Yao, "Hahn-Banach extension and optimization related to
.xed point properties and amenability", Journal of Nonlinear and Variational Analysis, vol. 1,
pp. 127--143, 2017. (Hahn-Banach)